The invention relates to simulation networks and more particularly to a network for simulating a frequency dependent negative resistor (FDNR).
In spite of increased success of active resistor-capacitor filters, voice-frequency passive filters remain useful because of two properties. First of all, a doubly terminated lossless ladder network and some other lossless topologies have low sensitivity to component variations. Secondly, passive filters operate bilaterally.
These same two properties also can be useful in active resistor-capacitor filters when passive filters having inductors are transformed into an active equivalent form. Such a transformation is used for synthesizing a passive filter by means of an active filter. As a part of the transformation, inductors are replaced by resistors, resistors are replaced by capacitors and capacitors are replaced by a simulation network which is a frequency dependent negative resistor. The FDNR can be realized as an active integrated circuit.
There are two important types of network response. One response is the current conducted through network terminals to which a potential is applied. A second response is the potential created across a pair of terminals when a current is conducted through the network connected between the terminals. These responses are characterized, respectively, by the impedance and the admittance of the respective networks. The name immittance is associated with those responses whenever the impedance and the admittance are not to be singled out individually. The word immittance can be considered to be a contraction for the expression "impedance or admittance" and is understood to mean a form of network response.
In the aforementioned transformation, each impedance of the filter is divided by a complex frequency variable s = j.omega. so that each inductor becomes a resistor, each resistor becomes a capacitor, and each capacitor becomes an element with an impedance proportional to 1/s.sup.2 in the transformed equivalent network. This latter element is the one called the frequency dependent negative resistor (FDNR).
Although FDNR circuits have been developed previously, such prior art FDNR circuits are relatively complex. In addition to the FDNR, the prior art circuits also include one or more additional equivalent circuit elements which cannot be separated from the FDNR and therefore make it either difficult or impossible to simulate some transformed passive filter arrangements.